Communication signals are typically subject to large amounts of additive noise, and some current spread-spectrum communications systems can function when the noise is a thousand times as large as the informational signal. This-noise can include random noise, multipath interference, and noise from other carrier signals in the vicinity. Chaotic signals are being considered as the possible basis of communication systems, because of a number of inherent advantages. Because chaotic signals are not periodic, they are resistant to multipath interference. Chaotic signals do not correlate strongly with other signals, so they are easier to separate from noise. A chaotic signal is unique to each chaotic attractor, so one can build multiuser communications systems from different attractors, even if generated from the same chaotic system. Chaotic signals are broad band, so they are less likely to interfere with other signals, and are detectable even if hidden below background noise.
Towards this end, there has been considerable work done on removing noise from chaotic signals. Much of this work has been based on embedding a chaotic signal in a phase space in order to eliminate noise. In general, phase-space based noise reduction techniques are only good if one can successfully embed the chaotic signal in phase space, so that the noise-corrupted point in the phase space is not too far from its noise-free location. Such techniques have typically proved able to reduce noise on the order of ten percent of the amplitude of the chaotic signal, although some techniques could handle noise as large as the chaotic signal itself. All of these techniques attempt to recover an exact copy of the original chaotic signal. For some applications, it may be useful just to approximate the original chaotic signal, as long as the approximation maintains some useful and recoverable property of the chaotic signal.
Accordingly, an object of the invention is to provide a novel scheme for spread-spectrum communication.
Another object is to increase the signal to noise performance of communications based on chaotic carrier signals.
In accordance with these and other objects hereinafter, the invention concerns a apparatus and method for signal generation, and an apparatus and method for detection of signal detection. In particular, the signal transmitter has a signal generator, the output of which corresponds to the trajectory of a preselected lossy chaotic system, a modulator disposed to modulate information onto the output of the signal generator so as to produce a resultant modulated signal and a propagator disposed to transmit the modulated signal. The signal detector has a signal receiver and an information storage member, the storage member being disposed to record preselected unstable periodic orbits extracted from a preselected lossy chaotic system, a selector disposed to compare portions of a signal received from the receiver to the preselected orbits to determine, for each of the portions of the signal, which of said orbits best matches said portions of the signal, and a processor disposed to concatenate the best matches into a resultant detected signal.
The extracted orbits stored in the detector are preferably the preselected orbits of the signal generator. In this manner, the concatenated best matches will correspond to the to the signal sent from the signal generator. Because only certain selected orbits of the chaotic system are used, the detector does not have to recover an exact copy of the trajectory of the original chaotic system that generated the orbits, making extraction simpler and more reliable, and permitting use of more conventional detection techniques which are effective to reduce noise, such as cross-correlation.